Here’s what the Catechism says:
REDEEMER/REDEMPTION: Jesus Christ, redeemer of mankind. Christ paid the price of his own sacrificial death on the cross to ransom us, to set us free from the slavery of sin, thus achieving our redemption. (571, 601; cf. 517, 1372).
571 The Paschal mystery of Christ’s cross and Resurrection stands at the center of the Good News that the apostles, and the Church following them, are to proclaim to the world. God’s saving plan was accomplished “once for all” by the redemptive death of his Son Jesus Christ.
601 The Scriptures had foretold this divine plan of salvation through the putting to death of “the righteous one, my Servant” as a mystery of universal redemption, that is, as the ransom that would free men from the slavery of sin. Citing a confession of faith that he himself had “received”, St. Paul professes that “Christ died for our sins in accordance with the scriptures.” In particular Jesus’ redemptive death fulfills Isaiah’s prophecy of the suffering Servant. Indeed Jesus himself explained the meaning of his life and death in the light of God’s suffering Servant. After his Resurrection he gave this interpretation of the Scriptures to the disciples at Emmaus, and then to the apostles.
**517 ** Christ’s whole life is a mystery of redemption. Redemption comes to us above all through the blood of his cross, but this mystery is at work throughout Christ’s entire life:
- already in his Incarnation through which by becoming poor he enriches us with his poverty;
- in his hidden life which by his submission atones for our disobedience;
- in his word which purifies its hearers;
- in his healings and exorcisms by which “he took our infirmities and bore our diseases”;
- and in his Resurrection by which he justifies us.
There is also a good article in This Rock magazine that addresses the very question you ask. It points out:
Through Christ God has provided the redemption necessary for salvation even to be offered, and that redemption is for all men without exception. Now all that needs to be done is to apply that redemption to each person, which is a way of describing salvation. It is repeated throughout Scripture that we are saved by grace through faith.
For the entire article, got to:
Salvation for Non-Christians Explained